Communication devices, systems, software and methods employing symbol waveform hopping

ABSTRACT

Systems, devices, and methods of the present invention facilitate secure communication by altering the set of symbol waveforms that may be in use in particular symbol times defined herein as Symbol Waveform Hopping. SWH may be enabled by selecting two or more modulation formats that have sufficiently comparable communication performance (e.g., occupied bandwidth and signal power efficiency), but characterized by symbol waveform alphabet that include different symbol waveform, so that the overall transmission/communication performance of the system is not significantly affected by switching between modulation formats. Some or all of the symbol waveforms in each alphabet may not be present in other alphabets.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and priority from U.S.Provisional Patent Application No. 62/848,279, filed on May 15, 2019,entitled “Communication Devices, Systems, Software and Methods employingSymbol Waveform Hopping”, the entire contents of which is herebyincorporated by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Award #1738453awarded by the National Science Foundation. The government has certainrights in the invention.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates in general to data transmission, and moreparticularly relates to transmitting data using multiple modulationformats to make the data more difficult for unintended recipients toreceive.

Background Art

For many purposes, there is a need to secure communications frominterception, or in some cases even from detection. This problem isdescribed as “low probability of intercept/low probability of detection”(LPI/LPD).

A first level of security is generally associated with encrypting thedata, transmitting and receiving the encrypted data, and decrypting thedata. Another level of security may be to vary the transmission channelover which the data is sent. For example, frequency-hopping spreadspectrum (FHSS) may be employed. FHSS sends data using multiple carrierfrequencies and switches between the multiple carrier frequencies usinga pseudorandom sequence known to the transmitter and receiver. FHSS isalso the basis for Code-Division Multiple Access (CDMA).

With the continuing increase in signal processing capabilities availableto adversaries, it is a continuing challenge to securely encrypt andtransmit with LPI/LPD. As such, there is a continuing need for system,devices, software, and methods that may be used to make it moredifficult for adversaries to intercept and access the data beingtransmitted through communication systems.

BRIEF SUMMARY OF THE INVENTION

Systems, devices, software, and methods of the present invention enablethe enhancement of LPI/LPD communication by switching between symbolwaveforms used to transmit data. Varying symbol waveforms duringtransmission presents a potential adversary with the problem of notknowing the format of a transmitted signal, as the symbol waveforms tobe recognized may change randomly and as often as every symbol time.

Unlike the prior art modulation formats, which are predominantly basedon constant amplitude sinusoids over each symbol time, the presentinvention enables the use of more general symbol waveforms, such aspolynomial symbol waveforms (PSWs), that allow for the creation of verydifferent modulation formats with comparable transmission/communicationperformance, thereby enabling symbol waveform variation duringtransmission without a loss of performance. The variation of symbolwaveforms used in the transmission of a bit stream is referred to hereinas “Symbol Waveform Hopping” (SWH). SWH may employ multiple symbolwaveform alphabets, each alphabet including multiple symbol waveformsthat may be different between the alphabets and switch between thedifferent symbol waveform alphabets during transmission times accordingto a sequence, e.g., pseudo-randomly, which is predetermined and knownto the transmitter and receiver.

SWH may be enabled by selecting two or more modulation formats that havesufficiently comparable transmission/communication performance (e.g.,occupied bandwidth and signal power efficiency) so that the overallcommunication performance of the system is not significantly affected byswitching between modulation formats as indicated by SWH. Also, thesetwo or more modulation formats should be sufficiently distinct that areceiver configured to detect one of these modulation formats will bepoorly suited to or unable to recognize the others. Similarly, the firstand second formats should be selected so that signals in each formatcannot be received and the original bit stream sufficientlyreconstituted by a third format. The modulation formats arecharacterized by symbol waveform alphabets including a set of differentsymbol waveforms that characterize the modulation format. Some or all ofthe symbol waveform in each alphabet may not be present in otheralphabets.

In various embodiments, a user and/or an automated process may provideto a transmitter and a receiver in a communication system used totransmit data a predetermined symbol waveform alphabet sequence and aplurality of symbol waveform alphabets to be used to transmit data viasymbol waveforms from the transmitter to the receiver. At least two ofthe symbol waveform alphabets may include one or more different symbolwaveforms as noted above. For any given application of the system, thealphabets may be chosen such that data sent via the symbol waveforms ineach alphabet can not be meaningfully detected or received using one ofthe other alphabets and that each alphabet has a sufficiently similartransmission/communication performance for the specific application andnot, necessarily in general.

Data being transmitted through the system is converted into a sequenceof symbol waveforms that are selected from the plurality of symbolwaveform alphabets based on the predetermined symbol waveform alphabetsequence, and then transmitted. The sequence of symbol waveforms may bereceived by the receiver and converted back into the data based on thepredetermined symbol waveform alphabet sequence. In various embodiments,a time-amplitude sequence corresponding to the data may be transmittedby sampling the sequence of symbol waveforms.

The plurality of symbol waveform alphabets used in the methods, systems,and apparatuses may be selected to have similartransmission/communication performance, such as similar OBW and biterror rate (BER) versus additive white Gaussian noise (AWGN)performance. In various embodiments, the plurality of symbol waveformalphabets may be selected to have a number of symbol waveforms equal toa power of two and/or the same number of symbol waveforms. Also, thesymbol waveforms may be sized to correspond to one symbol time or otherdata measure.

In various embodiments, the symbol waveform alphabets may be implementedas one or more lookup tables stored in computer readable medium, memory,or other storage that may be accessed, retrieved, and be otherwise madeavailable for use by the system. The symbol waveform alphabets may begenerated as a set of polynomial symbol waveforms and/or as symbolwaveforms representative of traditional modulation formats.

In various embodiments, a set of symbol waveform alphabets to transmitdata are identified, in which each alphabet includes at least one symbolwaveform and has similar overall signal transmission characteristics,but different sets of symbol waveforms from other alphabets. Uniqueidentifiers are assigned to each symbol waveform alphabet and a uniquebit string is associated with each symbol waveform in each alphabet.

In preparation for transmission, data is converted into a sequence ofbit strings and may be further converted to bit string subsequences. Thetransmitter and/or other processor upstream from the transmitter mayaccess the symbol waveform alphabet according to the predeterminedsymbol waveform alphabet sequence and select the symbol waveforms withinthe accessed symbol waveform alphabet corresponding to the bit stringsubsequences and provide the sequence of symbol waveforms fortransmission.

The predetermined symbol waveform alphabet sequence may be provided bythe transmitter to the receiver or by the receiver to the transmitter.Alternatively, or in addition, a management system may provide thepredetermined symbol waveform alphabet sequence to one or both thetransmitter and receiver. It will be appreciated that varying the sourceof the predetermined symbol waveform alphabet sequence may makeinterception more difficult.

In various embodiments, the predetermined symbol waveform alphabetsequence may not be transmitted, but may be generated at the transmitterand/or receiver based on an initiator code provide by the transmitter,receiver, or management system that results in the sequence beinggenerated by a sequence generator in the transmitter and receiver. Thelocal generation of the predetermined symbol waveform alphabet sequencemay increase the security of data passing through the system.

The present invention may be employed alone or in parallel with otherencryption techniques known to the art, including FHSS and bitstream/data encryption. In addition, the present invention may be usedwith single and/or parallel, i.e., multi-channel, transmissiontechniques.

As may be disclosed, taught, and/or suggested herein to the skilledartisan, the present invention addresses the continuing need forhardware and/or software systems, devices, and methods that securecommunications and provide LPI/LPD enhancements.

BRIEF DESCRIPTION OF THE DRAWINGS

Advantages of embodiments of the present invention will be apparent fromthe following detailed description of the exemplary embodiments thereof,which description should be considered in conjunction with theaccompanying drawings, which are included for the purpose of exemplaryillustration of various aspects of the present invention to aid indescription, and not for purposes of limiting the invention.

FIG. 1 illustrates exemplary data transmission systems.

FIG. 2 illustrates exemplary data transmission systems.

FIG. 3 illustrates an exemplary polynomial symbol waveform alphabetcorresponding to the symbol waveforms used by standard 8-PSK with RootRaised Cosine (RRC) filtering, referred to herein as Poly_8PSK.

FIG. 4 is an exemplary BER v AWGN plot for the Poly_8PSK alphabet.

FIG. 5 illustrates an exemplary first polynomial symbol waveformalphabet, referred to herein as MC_OBW_Opt_A.

FIG. 6 is an exemplary BER v AWGN plot for the MC_OBW_Opt_A alphabet.

FIG. 7 illustrates an exemplary polynomial symbol waveform alphabet,referred to herein as MC_OBW_Opt_B.

FIG. 8 is an exemplary BER v AWGN plot for the MC_OBW_Opt_B alphabet.

In the drawings and detailed description, the same or similar referencenumbers may identify the same or similar elements. It will beappreciated that the implementations, features, etc., described withrespect to embodiments in specific figures may be implemented withrespect to other embodiments in other figures, unless expressly stated,or otherwise not possible.

DETAILED DESCRIPTION OF THE INVENTION

Aspects of the invention are disclosed in the specification and relateddrawings, which may be directed to specific embodiments of theinvention. Alternate embodiments may be devised without departing fromthe spirit or the scope of the invention. Additionally, well-knownelements of exemplary embodiments of the invention will not be describedin detail or will be omitted so as not to obscure the relevant detailsof the invention. Further, to facilitate an understanding of thedescription, a discussion of several terms used herein may be included.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration” and not as a limitation. Any embodimentdescribed herein as “exemplary” is not necessarily to be construed aspreferred or advantageous over other embodiments. Likewise, the term“embodiments of the invention” does not require that all embodiments ofthe invention include the discussed feature, advantage or mode ofoperation.

Further, many embodiments are described in terms of sequences of actionsto be performed by, for example, elements of a computing device. It willbe recognized that various actions described herein can be performed byspecific circuits (e.g., application specific integrated circuits(ASICs)), by field programmable gate arrays, by program instructionsbeing executed by one or more processors, or by a combination thereof.Additionally, sequence(s) of actions described herein can be consideredto be embodied entirely within any form of computer readable storagemedium having stored therein a corresponding set of computerinstructions that upon execution would cause an associated processor toperform the functionality described herein. Thus, the various aspects ofthe invention may be embodied in a number of different forms, all ofwhich have been contemplated to be within the scope of the claimedsubject matter. In addition, for each of the embodiments describedherein, the corresponding form of any such embodiments may be describedherein as, for example, “logic configured to” perform the describedaction. For example, it will be appreciated that transmitters,receivers, management systems, and other devices in systems of thepresent invention may include one or more processors, memory, storage,input and components, communication interfaces, as well as othercomponents that may be interconnected as desired by the skilled artisanvia one or more buses and circuit boards, cards, etc.

Systems, devices, software, and methods of the present invention enablethe enhancement of LPI/LPD communication by switching between symbolwaveforms used to transmit data. Varying symbol waveforms duringtransmission presents a potential adversary with the problem of notknowing the format of a transmitted signal, as the symbol waveforms tobe recognized may change randomly and as often as every symbol time.

Unlike the prior art modulation formats, which are based on constantamplitude sinusoids with stationary spectrums that provide verydifferent communication performance if the waveform design issignificantly altered e.g. by altering phase separation, the presentinvention enables the use of symbol waveforms, such as polynomial symbolwaveforms (PSWs), that allow for the creation of different modulationformats with comparable communication performance, thereby enablingsymbol waveform variation during transmission without a loss ofperformance. Modulation formats may be represented as symbol waveformalphabets that include one or more symbol waveforms. The symbolwaveforms may be based on constant amplitude sinusoids with stationaryspectrums as well as varying amplitude waveforms with non-stationaryspectrums to form alphabets including different symbol waveforms, butprovide similar transmission/communication performance or sufficientperformance such that data may be transmitted via the alphabet andreceived by a receiver in a specific application.

The variation of symbol waveforms and specifically waveform alphabetsduring the transmission of a bit stream is referred to herein as “SymbolWaveform Hopping” (SWH). SWH employs multiple symbol waveform alphabetsand switches between the different symbol waveform alphabets duringtransmission times according to a predetermined symbol waveform alphabetsequence, e.g., pseudo-randomly, known to the transmitter and receiver.For example, if two alphabets A and B are used, the predeterminedsequence may be 3A2B1A3B . . . as selected by a user or generatedrandomly or otherwise. In addition, the alphabet sequence may be variedat random or periodic intervals as may be desired. Predetermined merelymeans that the sequence is known to the transmitter before transmissionand to the receiver before reception sufficiently to enable transmissionof the data using the sequence. In various embodiments, the sequence mayonly be known to the transmitter and receiver transmitting the data andnot to the management system or other devices or users, or to someportion of those entities.

SWH may be enabled by selecting two or more modulation formats that havesufficiently comparable communication performance for an application(e.g., occupied bandwidth and signal power efficiency) so that theoverall communication performance of the system is not significantlyaffected by switching between modulation formats as indicated by SWH. Inaddition, the two or more modulation formats used for SWH should besufficiently distinct that a receiver configured to detect one of thesemodulation formats will be poorly suited to or unable to recognizesignals in the other formats. Similarly, the first and second formatsshould be selected so that signals in each format cannot be received andthe original bit stream sufficiently reconstituted by a third format.

Some or all of the symbol waveforms in each alphabet may not be presentin other alphabets. The skilled artisan will appreciate that thedifferentiation between the symbol waveforms in each alphabet may dependupon various factors, such as the network, application, etc. Forexample, it may be desirable to include some alphabets with some or manysimilar waveforms for some applications and no similar waveforms inother applications.

For any given application of the system 10, the alphabets may be chosensuch that data sent via the symbol waveforms in each alphabet can not bemeaningfully detected or received using one of the other alphabets andthat each alphabet has a sufficiently similar transmission/communicationperformance for the specific application and not, necessarily ingeneral. For example, if alphabet A and B can be reliably transmitted1000 km and 2000 km, respectively, then the performance of thesealphabets may be similar and data can be reliably transmitted andreceived using both alphabets for transmission distance less than 1000km and not for distance greater than 1000 km. It will be appreciatedthat it may be possible to detect signals sent with the variousalphabets and convert the signal into bits, but the selection of thealphabets is such that the data can not be received, i.e., recoveredfrom the signal and bits in useful manner, using the other alphabets.

The difference between the symbol waveforms in each alphabet can rangefrom one to all, as the variations in the symbol waveforms merely needsto be sufficient that data sent via each alphabet can not be determinedby detecting the other alphabets. In various embodiments, it may bepossible to have two or more alphabets, e.g. A and B, of a larger set ofalphabets, A-C, where data sent via A or B could be determined by A orB, so long as alphabet C could not determine the data sent using A or Band data sent using C could not be determined using A or B.

Spiral and polynomial based modulation techniques may be useful forgenerating symbol waveforms in the present invention. These techniquesmay be used to produce formats with non-stationary spectra, whichprovides additional freedom in generating symbol waveforms that providecomparable communication performance. For additional information onspiral and polynomial waveform design and modulation, see, for example,U.S. Pat. No. 8,472,534 entitled “Telecommunication Signaling UsingNon-Linear Functions”, U.S. Pat. No. 8,861,327 entitled “Methods andSystems for Communicating”, U.S. Pat. No. 10,069,664 entitled “SpiralPolynomial Division Multiplexing” (SPDM), and U.S. patent applicationSer. No. 16/735,655 filed Mar. 6, 2020 entitled “Devices, Systems, AndMethods Employing Polynomial Symbol Waveforms”, the contents of whichare herein incorporated by reference in their entirety, except for theclaims and any disclosure contrary to this disclosure, and Prothero, J.,Islam, K. Z., Rodrigues, H., Mendes, L., Gutiérrez, J., & Montalban, J.(2019), Instantaneous Spectral Analysis. Journal of Communication andInformation Systems, 34(1), 12-26, https://doi.org/10.14209/jcis.2019.2.

FIG. 1 shows exemplary systems 10 including exemplary transmitter 12 andreceiver 14 pairs that may be used in transmission or communicationsystems, such as further shown in FIG. 2. Bits, usually representingdata/information, being transmitted through the system 10 may beconverted to symbol waveforms in a channel encoder 16 section of thetransmitter 12, as well as have other signal processing, e.g., forwarderror correction, performed to prepare the transmission signal.

The symbol waveforms may then be used to modulate a carrier provided bya carrier source 20 using an external modulator 22 as shown in FIG. 1 orto directly modulate the carrier source 20 to produce the transmissionsignal. The symbol waveforms may be transmitted using multiple carrierssimultaneously, such as when implemented with Instantaneous SpectralAnalysis (“ISA”), see U.S. Pat. No. 10,069,664 incorporated above.

The encoder 16 and decoder 18 are shown as single blocks in FIG. 1.However, the encoder 16 and decoder 18 may include one or morestages/components that are used to process the information passingthrough the system 10. The encoding and decoding function may beperformed inside and/or outside the transmitter 12 and receiver 14, asdesired by the skilled artisan.

At the receiver 14, a detector 24 may detect the transmission signal andprovide the transmission signal to signal processors, which may includethe decoder 18 to perform any decoding necessary to output the bits. Thebits output from the system 10 may be in the form of data and clocksignals, or otherwise. In various embodiments, the system 10 may belocally and/or remotely monitored and/or controlled by a managementsystem 25 as is known in the art. The system 10 may be deployed as partof a local private point-to-point network, as well as part of the globalterrestrial and satellite infrastructure and managed accordingly.

FIG. 2 shows exemplary systems 10 that include a plurality oftransmitters 12 and receivers 14 that may be deployed in varioustransmission and communication systems employing various wired andwireless transmission media 26 and may include symbol waveform hoppingtechnology of the present invention. For example, systems 10, such asshown in FIG. 1 and FIG. 2 and other systems, may be deployed in variouselectrical and optical wired transmission and communication networks, aswell as satellite and terrestrial wireless networks. In various systems,the transmission signals may be multiplexed in a multiplexer 28 beforetransmission and may require demultiplexing before detection in ademultiplexer 30 after transmission, as is commonly performed in wiredand wireless systems carrying multiple channels.

The symbol waveform alphabets that may be used in the system 10 may bemaintained proximate or in the various transmitters 12, receivers 14,and management system 25, as well as in other locations that may beaccessed by user and the management system 25, via an automated processor otherwise, and provided to the transmitters 12 and receivers 14. Itwill be appreciated that the user may be the owner of the data beingtransmitted, a system administrator or operator, a trusted third party,etc. as decided by the parties involved.

In various embodiments, the symbol alphabets that are to be used in thesystem 10 may be maintained in a computer readable storagemedium/memory/storage in the transmitters 12 and receivers 14, such asstored in one or more look-up tables or other formats that may beaccessed by processors running on the devices. The alphabets and thealphabet sequence may be locally and/remotely installed or provided tothe equipment at various points in time ranging from the initialdeployment of the equipment to just prior to use in transmission.

In various embodiments, the SWH technology of the present inventiondescribed herein may be implemented as follows:

-   -   1. Identify a set of symbol waveform alphabets to be used to        transmit bits in the hardware and/or software system. The        alphabets may be designed using techniques disclosed in U.S.        patent application Ser. No. 16/735,655, incorporated above, or        other techniques. The set of symbol waveform alphabets may be        designed to have similar OBW, signal power efficiency, and/or        other characteristics, so that the overall signal transmission        characteristics are not sufficiently altered by switching        between symbol waveform alphabets to prevent efficient        transmission of the underlying data. Simulation software and/or        hardware transmission tests may be used to compare the        performance characteristics of various symbol waveform        alphabets. Modulation formats that have similar OBW and bit        error rate (BER) versus additive white Gaussian noise (AWGN)        performance may be suitable candidates for various SWH        applications. The skilled artisan may vary the criteria used for        selecting modulation formats depending upon the specific        application. For example, in various embodiments, the number of        symbol waveforms in each alphabet may be selected to be a power        of two or not. Similarly, the symbol waveform alphabets may or        may not include the same number of symbol waveforms.    -   2. Assign a unique identifier to each symbol waveform alphabet.    -   3. Associate a unique bit string to each symbol waveform in each        alphabet.    -   4. Prior to communicating a message, i.e., information/data,        establish a symbol waveform alphabet sequence that is known, or        predetermined, to transmitter(s) and receiver(s) involved in the        message communication identifying the particular symbol waveform        alphabet to be used to generate symbol waveforms at particular        times for sending the message. This sequence may be expressed in        terms of the unique symbol waveform alphabet identifiers or        otherwise and be a pseudo-random sequence or other sequence.    -   5. Convert the message into at least one bit string for        communication.    -   6. Convert the bit string(s) in subsequences of bits. For        example, the length of subsequence may be set to the log base        two of the number of symbol waveforms in each symbol waveform        alphabet in the set of symbol waveform alphabets. Each such bit        string subsequence may be transmitted in one symbol time.    -   7. Retrieve, at the start of each symbol time, by the        transmitter(s) and receiver(s), the symbol waveform alphabet        according to the predetermined symbol waveform alphabet sequence        provided to the transmitter(s) and receiver(s). In an exemplary        implementation, the symbol waveform alphabets may be stored in        lookup tables or other formats in hardware, e.g., computer        readable medium, memory, or other storage, either in or        proximate the transmitters and receivers. Each symbol waveform        may be represented by samples taken by evaluating the symbol        waveform over the symbol time duration.    -   8. Select, at the start of each symbol time, the symbol waveform        within the selected symbol waveform alphabet that corresponds to        a bit substring.    -   9. Transmit, by the transmitter, the waveform corresponding to        the selected symbol waveform. The symbol waveforms to be        transmitted may also be time sampled to produce a time-amplitude        sequence prior to transmission.    -   10. Receive, by the receiver, the transmitted waveform. In an        exemplary embodiment, the receiver may use minimum distance        signal detection.    -   11. Convert the received waveform into the bit substring based        on the symbol waveform alphabet according the alphabet sequence.    -   12. Reassemble the message from the received and converted bit        substrings.

One of ordinary skill will appreciate that #1-3 of the above proceduremay be performed at most times in advance of the actual datatransmission in the system 10 and #4 may be performed up to the time ofdata transmission. For example, the symbol waveform alphabets may begenerated and/or selected by any skilled practitioners associated withany entity involved in the data transmission including the data ownerand/or transmission system/network operator, information technologyadministrator, etc. using one or more of the various techniquesdescribed in the reference cited and incorporated herein.

In various embodiments, the predetermined symbol waveform alphabetsequence may or may not be transmitted between the transmitter 12 andreceiver 14 and/or from the management system 25. For example, thepredetermined symbol waveform alphabet sequence may be generated viaprocessor in or near the transmitter 12 and/or receiver 14 based on aninitiator code provided by the transmitter 12, receiver 14, ormanagement system 25 that results in the predetermined symbol waveformalphabet sequence being locally generated and known to each device. Thelocal generation of the predetermined symbol waveform alphabet sequencemay increase the security of data passing through the system 10.

In operation, SWH may be applied to new or existing modulation formats.For example, the aforementioned method was applied to generate symbolwaveforms for use in combination with, or in lieu of, 8 state phaseshift keying (8PSK) format. For purposes of demonstration andcomparison, a polynomial symbol waveform (symbol waveform) alphabet wasgenerated that is representative of a standard 8PSK format with RootRaised Cosine (RRC) filtering by starting with 8 sinusoidal polynomialshaving even phase offsets between them, then convolving with apolynomial corresponding to an RRC with α=0.1, referred to herein asPoly_8PSK.

FIG. 3 illustrates the resulting polynomial symbol waveform alphabetcorresponding to Poly_8PSK. As can be seen, the waveforms are symmetricabout the x-axis and offset in phase. Transmission of a signal employingPoly8PSK was simulated using MATLAB. The occupied bandwidth (OBW) of thesignal was determined using the MATLAB obw function based on a Fourieranalysis of the signal to be 2.3 MHz.

For comparison, the OBW of the Poly_8PSK was also calculated using asoftware spectrum analyzer (SSA), such as described in U.S. ProvisionalPatent Application No. 62/848,280 filed May 15, 2019 entitled Devices,Systems, and Software including Signal Power Measuring and Methods andSoftware for Measuring Signal Power, which is incorporated by referencein its entirety, except for the claims and any disclosure contrary tothis disclosure. The SSA, unlike Fourier analysis, does not require thesignal to have a stationary spectrum, which enables the SSA to beapplied to a wider range of modulation formats, e.g., polynomial symbolwaveform with non-stationary spectrums and constant amplitude sinusoidwith stationary spectrum alphabets.

The OBW calculated using the SSA was also found to be 2.3 MHz. Theagreement between the Fourier-based OBW calculation and the SSA wasexpected because the Poly_8PSK is a stationary spectrum format just like8PSK and the other constant amplitude sinusoidal-based modulationformats.

FIG. 4 shows exemplary results for bit error rate (BER) versus additivewhite Gaussian noise (AWGN) calculations for the Poly_8PSK. As can beseen, the BER vs. AWGN performance agrees well with the theoretical BERv AWGN performance for 8PSK.

Given the Poly_8PSK modulation format as a baseline, the presentinvention was applied to develop additional symbol waveforms that may beappropriately used to perform the SWH method. A first modulation formatwas developed using the techniques described in U.S. Patent ApplicationNo. U.S. Provisional patent application Ser. No. 16/735,655,incorporated above and optimized using a Monte Carlo method to have anOBW similar to Poly_8PSK, while retaining from prior design BER vs. AWGNperformance (signal power efficiency) greater than Poly_8PSK.

FIG. 5 shows the polynomial symbol waveform alphabet generated as thefirst modulation format, referred to herein as MC_OBW_Opt_A. As can beseen in the figure, while somewhat resembling the Poly_8PSK alphabet(FIG. 3), the MC_OBW_Opt_A alphabet has a different structure in that itincludes symbol waveforms with forms, or shapes, that are significantlydifferent than the symbol waveforms in the Poly_8PSK alphabet. Inaddition, some of waveforms are non-sinusoidal with a non-stationaryspectrum. As such, the SSA was used to calculate the OBW and variouscalculations were performed using Monte Carlo techniques to optimize thealphabet for use with SWH.

The calculations were performed according to the following process:

-   -   The simulated symbol time was 1 microsecond in all calculations.    -   All alphabets were of size 8, corresponding to 3 bits per        symbol.    -   Each polynomial symbol waveform was sampled 25 times in every        symbol time.    -   OBW was measured in terms of 99% single-sided power occupancy,        on streams of 15,000 simulated bits transmitted.    -   In all polynomial symbol waveform alphabets studied, all        polynomials were individually power normalized to the same value        of 0.1, in arbitrary units.    -   Signal power efficiency was measured in terms of BER vs. AWGN        over a simulated signal length of 1.5 million bits transmitted        per AWGN level.    -   For purposes of logarithmic plotting, a bit error rate (BER) of        zero was mapped to 10e-6.    -   All polynomial symbol waveform alphabets were Gray coded to        maximize BER performance in the presence of symbol detection        errors induced by AWGN.

FIG. 6 shows the BER v AWGN results for the MC_OBW_Opt_A symbol waveformalphabet. As can be seen, the performance is approximately 2-3 dB betterthan Poly_8PSK. In addition, the OBW performance of MC_OBW_Opt_A is 2.3MHz, which is substantially the same as Poly_8PSK.

FIG. 7 shows a second modulation format, referred to herein asMC_OBW_Opt_B, that was generated for use in SWH methods of the presentinvention. The second modulation format was generated starting from thePoly_8PSK and then optimizing the design of the alphabet for BER v AWGNperformance, while maintaining the OBW of the Poly_8PSK alphabet. As canbe seen in FIG. 7, the MC_OBW_Opt_B alphabet, while resembling thePoly_8PSK alphabet (FIG. 3), has a different structure in that itincludes symbol waveforms with forms that are significantly differentthan the symbol waveforms in the Poly_8PSK alphabet and also has somenon-sinusoidal waveforms.

FIG. 8 shows the BER v AWGN results for the MC_OBW_Opt_B. As can beseen, the performance is also approximately 2-3 dB better thanPoly_8PSK. The OBW performance of MC_OBW_Opt_B remains 2.3 MHz, which isconsistent with OBW for Poly_8PSK.

The similar transmission/communication performance of the MC_OBW_Opt_Aand MC_OBW_Opt_B alphabets, while having different waveforms, suggeststhat various combinations of the two alphabets may be useful forimplementing SWH technology in various systems. It will be appreciatedthat for applications in which Poly_8PSK may provide acceptablecommunication performance, SWH may be implemented using Poly_8PSK alongwith MC_OBW_Opt_A and MC_OBW_Opt_B based on the different symbolwaveforms in each alphabet. For example, systems that currently employ8PSK modulation formats may be candidates for SWH technology employingthese alphabets.

One of ordinary skill will further appreciate that other alphabets withsimilar transmission performance characteristics may be used incombination with, or in lieu of, one, some, or all of these alphabets.It will be further appreciated that 8-symbol alphabets have been usedherein for exemplary purposes. SWH may be based on other alphabet sizes,e.g., 4, 16, or 64, 128, 512 symbol waveforms, and other modulationformats. In some applications, it may be desirable to employ variouscombinations of stationary and/or nonstationary waveforms in SWHembodiments, depending upon channel conditions, data throughputrequirements, or other considerations.

The foregoing description and accompanying drawings illustrate theprinciples, preferred embodiments and modes of operation of theinvention. However, the invention should not be construed as beinglimited to the particular embodiments discussed above. Additionalvariations of the embodiments discussed above will be appreciated bythose skilled in the art.

Therefore, the above-described embodiments should be regarded asillustrative rather than restrictive. Accordingly, it should beappreciated that variations to those embodiments can be made by thoseskilled in the art without departing from the scope of the invention asdefined by the following claims.

What is claimed is:
 1. A method of data transmission, comprising:providing, via at least one of a processor and a user, to a transmitterand a receiver in communication to transmit data via one data stream, apredetermined symbol waveform alphabet sequence including a plurality ofsymbol waveform alphabets, each symbol waveform alphabet including aplurality of symbol waveforms, where data transmitted in at least onesymbol waveform alphabet can not be received by the receiver using theother symbol waveform alphabets, and each alphabet having sufficienttransmission performance to be used to transmit the data from thetransmitter to the receiver; converting the data into a sequence ofsymbol waveforms selected from the plurality of symbol waveformalphabets including the at least one symbol waveform alphabet that cannot be received by the receiver using the other symbol waveformalphabets according to the predetermined symbol waveform alphabetsequence; transmitting, by the transmitter, the sequence of symbolwaveforms; receiving, by the receiver, the transmitted sequence ofsymbol waveforms; and, converting the received sequence of symbolwaveforms into the data based on the predetermined symbol waveformalphabet sequence.
 2. The method of claim 1, where the plurality ofsymbol waveform alphabets are selected to have similar transmissionperformance.
 3. The method of claim 1, where the plurality of symbolwaveform alphabets are selected to have similar occupied bandwidth (OBW)and bit error rate (BER) versus additive white Gaussian noise (AWGN)performance.
 4. The method of claim 1, where the plurality of symbolwaveform alphabets are selected to have a number of symbol waveformsequal to a power of two.
 5. The method of claim 1, where the pluralityof symbol waveform alphabets are selected to have the same number ofsymbol waveforms.
 6. The method of claim 1, further comprising:constructing a time-amplitude sequence corresponding to the data bysampling the sequence of symbol waveforms, where the time-amplitudesequence is transmitted and received.
 7. The method of claim 1, whereeach symbol waveform is transmitted in one symbol time.
 8. The method ofclaim 1, where the plurality of symbol waveform alphabets is provided asat least one lookup table.
 9. The method of claim 1, where convertingthe received waveform includes looking up the received waveform in alookup table for the symbol waveform alphabet.
 10. The method of claim1, where no two symbol waveform alphabets include all of the same symbolwaveforms.
 11. The method of claim 1, where providing the plurality ofsymbol waveform alphabets comprises: identifying a set of symbolwaveform alphabets to transmit data having similar overall signaltransmission performance, with no two alphabets including all of thesame symbol waveforms; assigning a unique identifier to each symbolwaveform alphabet; and associating a unique bit string to each symbolwaveform in each alphabet.
 12. The method of claim 1, where transmittingthe sequence of symbol waveforms comprises: converting the data into asequence of bit strings for transmission; converting the bit stringsinto bit string subsequences; accessing the symbol waveform alphabetsaccording to the predetermined symbol waveform alphabet sequence; andselecting the symbol waveforms within the accessed symbol waveformalphabet that corresponds to the bit string subsequences to provide thesequence of symbol waveforms for transmission.
 13. The method of claim1, where the predetermined symbol waveform alphabet sequence is providedby at least one of the transmitter providing the predetermined symbolwaveform alphabet sequence to the receiver and the receiver providingthe predetermined symbol waveform alphabet sequence to the transmitter.14. The method of claim 1, where a management system provides thepredetermined symbol waveform alphabet sequence to the receiver.
 15. Themethod of claim 1, where the predetermined symbol waveform alphabetsequence is randomly generated.
 16. The method of claim 1, where thesymbol waveforms in at least two symbol waveform alphabets aresufficiently distinct that the receiver configured to detect one of thesymbol waveform alphabets cannot reliably receive the data transmittedin the other symbol waveform alphabets.
 17. The method of claim 1, wherethe symbol waveforms in at least two symbol waveform alphabets aresufficiently distinct that the receiver configured to detect a thirdsymbol waveform alphabet cannot reliably detect the data transmittedusing two other symbol waveform alphabets.
 18. The method of claim 1,where the symbol waveforms are selected from the plurality of symbolwaveform alphabets by switching between the symbol waveform alphabetsused to convert the data based on the predetermined symbol waveformalphabet sequence.
 19. A system comprising: a transmitter to receive amessage, and transmit the message as a sequence of symbol waveforms viaone transmission channel, the symbol waveforms selected from a pluralityof symbol waveform alphabets according to a predetermined waveformalphabet sequence, where the message transmitted in at least one symbolwaveform alphabet that can not be received by a receiver using the othersymbol waveform alphabets, and each alphabet having sufficienttransmission performance to transmit the message from the transmitter tothe receiver; and the receiver to receive the sequence of symbolwaveforms, and convert the received symbol waveforms into the messagebased on the predetermined sequence waveform alphabet sequence and theplurality of symbol waveform alphabets, and output the message.
 20. Anon-transitory computer readable medium storing instructions, theinstructions comprising: one or more instructions which, when executedby one or more processors, cause the one or more processors to: converta message into a sequence of symbol waveforms in one data stream, thesymbol waveforms selected from a plurality of symbol waveform alphabetsaccording to a predetermined sequence of the plurality of symbolwaveform alphabets, where the message transmitted in at least one symbolwaveform alphabet can not be received by a receiver using the othersymbol waveform alphabets, and each alphabet having sufficienttransmission performance to transmit the message from a transmitter tothe receiver; and transmit, by the transmitter, the sequence of symbolwaveforms.
 21. The non-transitory computer readable medium of claim 20,where converting the message occurs in the transmitter.
 22. Thenon-transitory computer readable medium of claim 20, where the one ormore instructions further cause the one or more processors to: receive,by the receiver, the sequence of symbol waveforms, and convert thereceived symbol waveforms into the message based on the predeterminedsequence of the plurality of symbol waveform alphabets.